(\(\partial _k\)  is a shorthand for \(\partial /\partial x_k\) ). If a set \(\lbrace \lambda _1,\lambda _2,\lambda ,\kappa \rbrace \)  can be found such that \(\Phi (\mathbf {x})\)  fulfills the integrability condition \(\partial _2\partial _1\Phi =\partial _1\partial _2\Phi \) , then a NEP exists. Early successful examples are the complex Ginzburg–Landau equation (CGLE) [1]}, [2]} and the FitzHugh–Nagumo (FHN) model [3]}, [4]} The knowledge of a NEP for FHN units has greatly simplified the dynamical analysis of reaction–diffusion [5]}, [6]}, [7]} and network [8]}, [9]}, [10]} FHN models, as well as the study of stochastic resonance in some extended systems [6]}, [12]}.. This scheme has been later reformulated [13]}, extended [14]}, and exploited in many interesting cases [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}.
